Question

If \(R\) and \(L\) denote resistance and inductance of a material, then the dimension of \(LR\) will be:

• A. \( M^2 L^4 T^{-5} A^{-4} \)
• B. \( M L T A^{-1} \)
• C. \( M^0 L^0 T^0 A^0 \)
• D. \( M^{-1} L^4 T A^{-3} \)

Hint:

Always break derived quantities into fundamental quantities (like \(V, I\)) to find dimensions quickly.

Answer 1

The Correct Option is A

Step 1: Dimension of resistance.
\[ R = \frac{V}{I} \] \[ [R] = \frac{ML^2T^{-3}A^{-1}}{A} = ML^2T^{-3}A^{-2} \]

Step 2: Dimension of inductance.
\[ L = \frac{V}{(dI/dt)} \] \[ [L] = \frac{ML^2T^{-3}A^{-1}}{AT^{-1}} = ML^2T^{-2}A^{-2} \]

Step 3: Multiply dimensions.
\[ [LR] = (ML^2T^{-3}A^{-2})(ML^2T^{-2}A^{-2}) \]

Step 4: Simplify powers.
\[ [LR] = M^2 L^4 T^{-5} A^{-4} \]

Step 5: Final conclusion.
\[ \boxed{M^2 L^4 T^{-5} A^{-4}} \] Hence, correct answer is option (A).